Tissue-CSF boundaries between brain tissue and cerebrospinal fluid (CSF) occur primarily at an outer cortical surface and in interior regions of the brain at CSF-filled ventricles. Locating these surfaces is beneficial for some neurosurgical procedures, such as convection-enhanced drug delivery, since placement of infusion catheters too close to CSF boundaries is known to lead to poor dispersion of infusate in tissue, as the infusate flows into the less-resistive CSF-filled regions.
Large CSF-filled structures are easily distinguished from brain tissue in many MRI imaging sequences. At the cortical surface, however, thin sulci are often narrower than the resolution provided by MR imagery and, thus, are not reliably detected. Furthermore, the problem can be complicated by brain pathologies. In particular, edema in white matter can greatly alter signal levels, making it difficult to separate white matter from other tissues.
In order to overcome this limitation, conventional methods detect the thicker cortical gray matter, and then use topological knowledge to estimate a location of an outer surface of the detected gray matter. The problem is thus transformed into finding a reliable segmentation of the cortical gray matter.
The cortex generally has a consistent thickness of about 3 mm. However, it can be difficult to differentiate gray matter from white matter. This difficulty is often compounded by inhomogeneities in the RF fields, making it difficult or impossible to separate gray and white matter with a constant threshold value.
A common approach to tissue classification is to assign a label to each voxel, identifying it as white matter (WM), grey matter (GM), or CSF, based on the voxel's signal level. Threshold levels separating the tissues, for example, can be obtained from user input or estimated from the image histogram. Other methods may use different representations in an attempt to more accurately identify surfaces that separate the three categories. Deformable surface models describe the interface either as a parameterized mesh of triangles (see, e.g., M. Kass, A. Witkin, and D. Terzopoulos, “Snakes: Active Contour Models,” Intl. J. Comp. Vision, v. 1, pp. 312-333, 1988), or using level set methods, where a zero level set implicitly defines the boundary (X. Zeng, L. H. Staib, R. T. Shultz, and J. S. Duncan, “Segmentation and Measurement of the Cortex from 3D MR Images Using Coupled Surfaces Propagation,” IEEE Trans. Med. Imaging, v. 18, pp. 100-111, 1999). Deformable surface models can represent partial voxels, but are generally complicated to implement and computationally intensive to run.
Brain tissue classification methods that use MRI data as input can encounter difficulties. These difficulties include a variation in signal response, and structures that are smaller than the sampling rate. These issues are described below.
MRI data used for brain tissue classification often contain some amount of artifact or distortion due to inhomogeneities in the radio frequency (RF) fields and magnetic susceptibility variations in the tissue being imaged. These effects give rise to small variations in the signal intensity that depend on the position of the sample location. These types of distortions are usually modeled as a multiplicative slowly-varying ‘gain’ field that modifies the expected signal values, e.g., M(x, y, z)=G(x, y, z)×I(x, y, z), where M denotes the measured signal, I is the undistorted signal, G represents the gain field, and “x” denotes an element-wise product. G is a low frequency field with values near unity. The intensity normalization step attempts to estimate the gain field and use it to restore the undistorted image.
A simple filtering method is often used to estimate G. A three-dimensional low-pass filter with a wide window can be applied to the image. Mean, median, and Gaussian filters have been used for this purpose. The low-pass result can be used to estimate the gain field.
The normalization problem is sometimes converted into the estimation of an additive ‘bias’ field B=log(G) by taking the logarithm of the expression. W. M. Wells, W. E. Grimson, R. Kikinis, F. A. Jolesz, “Adaptive Segmentation of MRI Data,” IEEE Trans. Med. Imaging, v. 15, pp. 429-442, 1996 suggested this approach, and an expectation maximization approach to solve the problem. In this method, normalization and tissue classification are combined. A statistical classification is performed, followed by bias field estimation using the classification results, and then the estimated bias is removed. These steps are iterated to converge on a normalized classification. Many variations of this strategy have been proposed. The difficulties with this method are that they are complicated to implement and relatively time-consuming to perform.
The second difficulty, structures too small to be detected at MRI resolution, occurs frequently at the cortical surface. Sufficiently large CSF-filled structures in the brain are usually easy to distinguish by their signal level alone. But the outer surface of the cortex, a GM-CSF boundary, has a complex geometry in which the CSF regions can be obscured. The topology is that of a highly folded sheet of gray matter about three millimeters thick. The CSF-filled space between the inner folds (sulci) may be very thin relative to the MRI resolution and thus may not always directly visible in typical MRI data. A sulcus may appear in MRI as a continuous region of gray matter.
Knowledge of the brain's topology is often used in cortical surface finding algorithms in order to locate thin sulci that are not directly visible. The inner cortical GM-WM boundary is more easily located, as the white matter structures inside the gyri are usually thick enough to be detected. Therefore, one can locate the cortical GM-WM boundary, and then use this information to help locate the GM-CSF boundary. X. Zeng, L. H. Staib, R. T. Shultz, and J. S. Duncan, “Segmentation and Measurement of the Cortex from 3D MR Images Using Coupled Surfaces Propagation,” IEEE Trans. Med. Imaging, v. 18, pp. 100-111, 1999, developed a level set method for segmenting the cortex that simultaneously evolves a pair of surfaces, one seeking the WM-GM cortical boundary and the other seeking the outer GM-CSF cortical surface. An additional constraint forces the two implicit surfaces to remain about three millimeters apart.
The coupled boundary level set approach has difficulty representing a pair of GM-CSF boundaries that are separated by less than the voxel resolution. X. Han, C. Xu, D. Tosun, and J. Prince, “Cortical Surface Reconstruction Using a Topology Preserving Geometric Deformable Model,” 5th IEEE Workshop on Math. Methods in Bio. Image Anal., Kauai, Hi., pp. 213-220, December 2001 propose a modified topology-preserving level set method to find the WM-GM cortical boundary only. They then compute the ‘skeleton’ of the cortical gray matter, which locates regions that are maximally distant from the WM-GM boundary on the GM side. This method locates the central plane within sulci well. The skeleton regions are then marked as cortical surface. This method performs well at locating the cortical surface, but the level set approach for locating the GM-WM boundary is compute-intensive, considering that the WM-GM interface is amenable to simpler classification methods, such as thresholding.